Question Number 87061 by john santu last updated on 02/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2x}\right)−\mathrm{cos}\:\left(\mathrm{x}\right)}{\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{2x}\right)−\mathrm{cos}\:\left(\mathrm{x}\right)}\:=\: \\ $$ Commented by jagoll last updated on 02/Apr/20 $$\mathrm{i}\:\mathrm{can}\:\mathrm{try} \\…
Question Number 152407 by imjagoll last updated on 28/Aug/21 Answered by Olaf_Thorendsen last updated on 28/Aug/21 $${f}\left({x},{y}\right)\:=\:\frac{\left({x}+{y}\right)\mathrm{sec}\left({x}+{y}\right)−{x}\mathrm{sec}{x}}{{y}} \\ $$$${f}\left({x},{y}\right)\:=\:\frac{\frac{{x}+{y}}{\mathrm{cos}\left({x}+{y}\right)}−{x}\mathrm{sec}{x}}{{y}} \\ $$$${f}\left({x},{y}\right)\:=\:\frac{\frac{{x}+{y}}{\mathrm{cos}{x}\mathrm{cos}{y}−\mathrm{sin}{x}\mathrm{sin}{y}}−{x}\mathrm{sec}{x}}{{y}} \\ $$$${f}\left({x},{y}\right)\:\underset{{y}\rightarrow\mathrm{0}} {\sim}\:\frac{\frac{{x}+{y}}{\mathrm{cos}{x}−{y}\mathrm{sin}{x}}−{x}\mathrm{sec}{x}}{{y}} \\…
Question Number 152362 by Tawa11 last updated on 27/Aug/21 $$\mathrm{f}\left(\mathrm{x}\right)\:\:\:=\:\:\:\begin{cases}{\mathrm{x}\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:,\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\:\:\mathrm{0}\:\:\:<\:\:\:\mathrm{x}\:\:\:\leqslant\:\:\:\mathrm{1}}\\{\:\:\:\:\:\:\mathrm{0}\:\:\:\:,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{if}\:\:\:\mathrm{x}\:\:\:=\:\:\:\mathrm{0}}\end{cases} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\:\mathrm{f}\:\:\:\mathrm{is}\:\mathrm{continous}\:\mathrm{but}\:\mathrm{not}\:\mathrm{of}\:\mathrm{bounded}\:\mathrm{variation} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86762 by Tony Lin last updated on 31/Mar/20 $${Find}\:{the}\:{sum}\:{of}\:{the}\:{series} \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{9}}+\frac{\mathrm{1}}{\mathrm{12}}+\centerdot\centerdot\centerdot \\ $$$${where}\:{the}\:{terms}\:{are}\:{the}\:{reciprocals} \\ $$$${of}\:{the}\:{positive}\:{integers}\:{whose}\:{only}\: \\ $$$${prime}\:{factors}\:{are}\:\mathrm{2}{s}\:{and}\:\mathrm{3}{s} \\ $$ Commented by Prithwish Sen…
Question Number 21223 by moadakennaf last updated on 16/Sep/17 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\pi−\mathrm{2}{x}\right)\mathrm{tan}\:\left({x}\right) \\ $$ Answered by dioph last updated on 16/Sep/17 $$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\pi−\mathrm{2}{x}}{\mathrm{cot}\:{x}}\:= \\ $$$$=\:\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{−\mathrm{2}}{−\mathrm{cosec}^{\mathrm{2}}…
Question Number 152287 by john_santu last updated on 27/Aug/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}\right)^{\frac{\mathrm{6}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}} \:=? \\ $$ Answered by iloveisrael last updated on 27/Aug/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}}…
Question Number 21194 by vivek last updated on 15/Sep/17 $$.\:\underset{{x}\rightarrow\mathrm{2}^{+} } {\mathrm{li}{m}}\:\left\{\frac{\left[{x}\right]^{\mathrm{3}} }{\mathrm{3}}\:−\left[\:\frac{{x}}{\mathrm{3}}\right]^{\mathrm{3}} \right\}\:{is}\:{equal}\:{to}\:… \\ $$$$ \\ $$ Commented by vivek last updated on 16/Sep/17…
Question Number 21179 by Joel577 last updated on 15/Sep/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{16}{x}^{\mathrm{2}} \:+\:\mathrm{4}{x}}\:−\:\sqrt{{x}^{\mathrm{2}} }\:−\:\sqrt{\mathrm{9}{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}} \\ $$ Answered by dioph last updated on 15/Sep/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\sqrt{\mathrm{16}+\frac{\mathrm{4}}{{x}}}\:−\:{x}\:−\:{x}\sqrt{\mathrm{9}+\frac{\mathrm{3}}{{x}}}…
Question Number 152239 by Tawa11 last updated on 26/Aug/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}\:\:+\:\:\mathrm{a}^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \:\:\:\:\:\:\:\:\:\:\left[\mathrm{for}\:\:\:\:\:\:\:\mathrm{a}\:\:<\:\:\mathrm{0},\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\:>\:\:\mathrm{0}\right] \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152211 by nitu last updated on 26/Aug/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{should}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{be}\:\infty\:\mathrm{or}\:\mathrm{is}\:\mathrm{it}\:\mathrm{DNE}. \\ $$$$\mathrm{my}\:\mathrm{main}\:\mathrm{question}\:\mathrm{is}, \\ $$$$\mathrm{when}, \\ $$$$\underset{{x}\rightarrow\mathrm{a}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\infty\: \\ $$$$\mathrm{does}\:\mathrm{it}\:\mathrm{not}\:\mathrm{exist}?\:\mathrm{is}\:\mathrm{it}\:\mathrm{DNE}? \\ $$…